Welcome to the homepage for Probability (Math 4600/6600)!

Probability is a deep and fascinating mathematical subject, with its own theory as well as connections to analysis, geometry, and combinatorics. In addition, it’s one of the most useful areas of applied mathematics, as entire careers and disciplines (e.g. actuarial science, quantitative finance, machine learning) rest on a firm understanding of the theory of probability. In addition, there are deep connections between probability and physics, explored mostly in the field of statistical physics.

This is a first course in probability, which will introduce you to the basics of the subject: discrete and continuous distributions, conditional probability and Bayes’ theorem, distribution functions and probability density functions, expectation and variance, sums of random variables, laws of large numbers and the central limit theorem, generating functions, Markov chains, and random walks.

Our text for the course is a lightly customized version of Grinstead and Snell, *Introduction to Probability*. This is an open-source book which you should download from the link above. During Fall 2021, the class meets twice a week at 2:20pm-3:35pm TR in Boyd 303. Office hours are virtual and scheduled via this page.

Homework, quizzes, and in-class projects will be assigned and collected via Gradescope. You can sign up for a Gradescope account for free and enroll in the course with course entry code **WY44YE**. We won’t use eLC at all for this course, since Gradescope and this webpage will give us everything we need. Tests will be taken in class, scanned, graded, and returned via Gradescope.

*Mathematica* will be an integral part of the course. UGA has a site license for *Mathematica* and you can get a copy for your laptop or home computer free of charge. I encourage you to work through some introductory material on *Mathematica*. Some of the homework assignments and projects will require you to write *Mathematica* programs, and it’s really helpful to be able to use a computer to check your work.

## Syllabus and Policies

Please examine the course syllabus. If you think you can get by with this copy, save a tree! Don’t print it out. The course syllabus lists the various policies for the course (don’t miss the attendance policy). The course is organized by day, with the updated plan for the course always visible on our shared Google Calendar. Every day, we’ll have a reading assignment before class. We’ll open class with a short quiz on the reading. Then we’ll have a discussion of the material in the book, followed by some in-class work that’s usually done in small groups. Office hours are online and scheduled through this link.

## Lecture Notes

Here are links to class notes and in-class problems. Classes with computer demonstrations have Mathematica notebooks posted here. Homework assignments which require Mathematica notebooks or data can also be found here.

- Lecture 1. Sample spaces, outcomes, and events. Basic properties. Tree diagrams and odds ratio.
- Lecture 2. Continuous probability distributions. Probability distribution function. Cumulative distribution function.
- Mathematica Notebook: Three Interesting Problems, Part 1.
- Mathematica Notebook: Three Interesting Problems, Part 2.
- Mathematica Notebook: Three Interesting Problems, Part 3

- Lecture 3. Combinatorics.
- Mathematica Notebook: The Birthday Problem and Pochhammer Symbols
- Mathematica Notebook: Stirling’s Approximation
- Mathematica Notebook: Derangements

- Lecture 4. Combinations.
- Mathematica Notebook: Binomial Distributions, Model Fitting, and Posterior Distributions.
- Mathematica Notebook: Applied Probability in Poker.